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Frequency- and Time-Localized Reconstruction from the Continuous Wavelet Transform

Reconstruct a frequency-localized approximation of Kobe earthquake data. Extract information from the CWT for frequencies in the range of [0.030, 0.070] Hz.

load kobe

Obtain the CWT of the data.

[wt,f] = cwt(kobe,1);

Reconstruct the earthquake data, adding the signal mean back into the transformed data.

xrec = icwt(wt,f,[0.030 0.070],'SignalMean',mean(kobe));

Plot and compare the original data and the data for frequencies in the range of [0.030, 0.070] Hz.

subplot(2,1,1)
plot(kobe)
grid on
title('Original Data')
subplot(2,1,2)
plot(xrec)
grid on
title('Bandpass Filtered Reconstruction [0.030 0.070] Hz')

Figure contains 2 axes. Axes 1 with title Original Data contains an object of type line. Axes 2 with title Bandpass Filtered Reconstruction [0.030 0.070] Hz contains an object of type line.

You can also use time periods, instead of frequency, with the CWT. Load the El Nino data and obtain its CWT, specifying the time period in years.

load ninoairdata
[cfs,period] = cwt(nino,years(1/12));

Obtain the inverse CWT for years 2 through 8.

xrec = icwt(cfs,period,[years(2) years(8)]);

Plot the CWT of the reconstructed data. Note the absence of energy outside the band of periods from 2 to 8 years.

figure
cwt(xrec,years(1/12))

Figure contains an axes. The axes with title Magnitude Scalogram contains 3 objects of type image, line, area.

Compare the original data with the reconstructed data for years 2 through 8.

figure
subplot(2,1,1)
plot(nino)
grid on
title('Original Data')
subplot(2,1,2)
plot(xrec)
grid on
title('El Nino Data - Years 2-8')

Figure contains 2 axes. Axes 1 with title Original Data contains an object of type line. Axes 2 with title El Nino Data - Years 2-8 contains an object of type line.